[SCL] two comments

[pat hayes]

>Tanel Tammet wrote:
>[...]
>>
>>Again, observe that when we write down formulas in abstract
>>syntax (and we have to do that in many places in the spec)
>>then the abstract syntax is used as a concrete syntax of
>>a special kind, which we happen to call "abstract",
>>since we have not defined the ascii etc aspects of
>>that language.
>
>Tanel,
>
>I think you've quite succinctly pointed out that what is at one level
>abstract is at another concrete. These various levels of "meta-ness"
>are there up and down the levels of description, and unavoidable. The
>thing to do is be sure to keep the levels clear and distinct.
>
>Murray


Guys, I was using the term 'abstract syntax' in a 
precise sense. It is a technical term introduced 
by John McCarthy; its not just a handy English 
phrase. See 
http://www-formal.stanford.edu/jmc/towards/node12.html
for a succinct introduction.  This approach was 
later formalized and systematized in the 
specification literature as 'term algebras', I 
believe, but we don't really need to get that 
formal.

The key motivational point is stated economically there:

" The predicates and functions whose existence 
and relations define the syntax, are precisely 
those needed to translate from the language, or 
to define the semantics. That is why we need not 
care whether sums are represented by a+b, or + 
ab, or (PLUS A B), or even by Gödel numbers 
7a11b."

which is exactly the utility for us, since we 
want to allow things like CG diagrams to count as 
logical syntax. In Murray's terminology, the AS 
is the highest meta-level anyone needs to go to 
in order to define a syntax and a model theory. 
(Splicing together documents, now, is another 
matter....)

Pat


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